Aging first-order rate constant

The inhibited esterase can also undergo aging, e.g. via net loss of the R-group to yield the negatively charged phos-phonyl adduct on the active site serine of the enzyme. Aging is characterized by a first-order rate constant, fcj, and the operational definition of this reaction is the time-dependent... 

Figure 20 Progress of intramolecular sulfurization of malabaricatriene (I) with depth in anoxic Cariaco basin sediments. Plot of the ratio of the concentrations of I to the sum of the concentrations of I + V (see Figure 19 for structures) as a function of sediment depth. The progress of transformation of I-V with increasing sediment depth is indicated by the steady decrease in the relative abundance of the precursor lipid (I). Inset plot of In ([ ]/([ ] + [V])) versus sediment age (= time), used to empirically determine the first-order rate constant for sulfur incorporation...

Table I. First Order Rate Constants for Al Aging...

Solutions were prepared having the following rn values 0.55, 0.94, 1.36, 1.84, 2.13, 2.47, 2.76, and 3.01 and were designated respectively solutions B, C, D, E, F, G, H, J. These solutions were allowed to age in a C02-free atmosphere near 25 °C for 254-259 days. At various intermediate aging times, aliquots of the solutions were analyzed for amounts of Ala, AP, and Alc as previously described. Also, first order rate constants... 

Figure 16.32. Anhenius plot of first-order rate constants of polythiophene ageing at 80°, 175°, 250° and 400°C from FTIR studies. Adapted from Synth. Met. 66, 33 (1994),with permission of Elsevier Science S.A., Lausanne.

An instructive example is the physiological variable serum creatinine. Creatinine is an endogenous metabolite formed from, and thus reflecting, muscle mass. Total body muscle mass is sufficiently constant to render measurement of serum creatinine useful for assessing actual renal function. The serum value of creatinine (R) is namely dependent on the continuous (zero-order) input of creatinine into the blood (A in) and its renal elimination rate, which is a first-order rate process (A out x ) In case of an extensive muscle breakdown, kin will temporarily increase. It may also be permanently low, for example in old age when muscle mass is reduced. Likewise, creatinine clearance may decrease for various reasons, described by a decrease in A out- An increase in creatinine clearance may occur as well, for example following recovery from renal disease. According to pharmacodynamic indirect response models. 

Studies of the disappearance of the octyl ester at pH 9.8 in sediment/water systems aged 3 days prior to pH adjustment are summarized in Figure 8. For the systems with p=0.013 and 0.005 (fractions sorbed =. 978 and. 945) the rate is pseudo first order, but the rate constant is 10 times smaller than the aqueous value (1.6x10 min ) at this pH. As was suggested for chlorpyrifos, this k value may be characteristic of the actual value of k. At p=0.001, (fraction sorbed = 0.78), the disappearance kinetics is not first order, but shows rapid disappearance of the aqueous ester, followed by disappearance of the sorbed ester at a rate similar to the studies with higher sediment to water ratios. 

The fits of the curves to the data are seen to display the rapid initial drop followed by the slower decline in endurance that is responsible for the curvature in the semilogarithmic plots. Scheme 2 can also potentially explain an initial increase in a measured property on aging by postulating that an initial concentration of intermediate X is present such that, with appropriate rate constants, the conversion of X into P will be faster than the transformation of P into X. A third feature of the above scheme is that when k12 and ki3 greatly exceed ki4, the property P will quickly reach a quasiequilibrium value of ki2/k z)F0 and then decay by first-order kinetics. When k 2 >> ki3, the kinetics will be first-order from the beginning, so that in limiting cases the conventional Equation 1 is obtained. 

In principle, if values of at could be determined n times throughout an accelerated aging experiment in which the empirical rate constant, k, is determined, then n simultaneous equations could be solved to yield the chemical rate constants, kt. However, in practice this is not feasible, and Equation 13 is of little analytical value. Nevertheless, our assumption that the property kinetic constant, k, is related linearly to chemical rate constants is verified. Thus, the apparent linearity of the empirical rate constant, kT in Equation 9, with respect to oxygen and acidity suggests the occurrence of chemical processes that are first order in oxygen and acidity. 

A comparison of the desorption rates at pH 7, shown in Figure 7 for the plutonium sorbed from fresh and aged solutions, indicates that the total desorption curve may be interpreted in terms of two different sorbed species. This is expressed in Equations 2, 3, and 4 as two first order processes. For both the fresh and aged systems, the relative quantities of the Ao(d or loosely-held species were almost identical, as were their desorption rate constants. It is likely that the A0<2 or tightly-held species were colloidal in size, since irreversibility is a widely known characteristic of colloid sorption. This was found to apply, for example, in the case of the sorption of colloidal americium on quartz (27). 

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